INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES UNKNOWN in .NET

Drawer qr-codes in .NET INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES UNKNOWN
10-3 INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO NORMAL DISTRIBUTIONS, VARIANCES UNKNOWN
Qrcode implementation on .net
use visual studio .net qr code iso/iec18004 implementation topaint qr code 2d barcode for .net
99 95 90 80 70 60 50 40 30 20 10
Qr Codes barcode library in .net
Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Percentage
recognize barcode on .net
Using Barcode decoder for .net vs 2010 Control to read, scan read, scan image in .net vs 2010 applications.
Figure 10-3 Normal probability plot of the arsenic concentration data from Example 10-6.
Bar Code writer with .net
generate, create barcode none in .net projects
5 1 0
QR encoder in visual c#
using barcode printer for visual .net control to generate, create qr-code image in visual .net applications.
PHX RuralAZ
Control qr code size with .net
to attach qr-code and denso qr bar code data, size, image with .net barcode sdk
10 20 30 40 50 Arsenic concentration in parts per billion
Control qr data in visual basic.net
to assign qr-codes and quick response code data, size, image with vb.net barcode sdk
3. H1: 1 2 4. 0.05 (say) 5. The test statistic is t* 0
Barcode Code 128 barcode library with .net
generate, create code-128c none with .net projects
B n1
EAN13 barcode library on .net
use vs .net crystal gtin - 13 generation tobuild ean-13 supplement 5 on .net
2 s1
Visual Studio .NET Crystal 2d data matrix barcode generating in .net
generate, create 2d data matrix barcode none with .net projects
2 s2
Assign linear 1d barcode on .net
using visual .net crystal toinsert linear 1d barcode with asp.net web,windows application
6. The degrees of freedom on t* are found from Equation 10-16 as 0 s2 1 an s2 2 2 n2 b 17.632 2 10 2 3 17.632 104 2 9 c 115.32 2 2 d 10 3 115.32 2 104 2 9
.net Vs 2010 identcode development on .net
using .net framework toembed identcode in asp.net web,windows application
1s2 1
Control ucc ean 128 size with .net
to embed ucc-128 and ean / ucc - 13 data, size, image with .net barcode sdk
n1 2 n1 1
ECC200 integration on office word
generate, create gs1 datamatrix barcode none for word projects
2 1s2 n2 2 2 n2 1
Control gs1 datamatrix barcode data with .net
to add data matrix 2d barcode and ecc200 data, size, image with .net barcode sdk
Therefore, using 0.05, we would reject H0: t* t0.025,13 2.160 0 7. Computations: Using the sample data we nd t* 0 B n1 x1 s2 1 x2 s2 2 n2
Control european article number 13 data for java
to include ean13 and ean 13 data, size, image with java barcode sdk
if t* 0
Web Form gs1 - 13 creator for .net
generate, create upc - 13 none with .net projects
t0.025,13
Control barcode code39 image with vb.net
using barcode integration for .net control to generate, create 3 of 9 barcode image in .net applications.
2.160 or if
Control ean / ucc - 14 data on .net
to paint gs1128 and ucc-128 data, size, image with .net barcode sdk
12.5 27.5 115.32 2 17.632 2 10 B 10
Barcode printing on objective-c
generate, create bar code none in objective-c projects
8. Conclusions: Because t* 2.77 t0.025,13 2.160, we reject the null hypoth0 esis. Therefore, there is evidence to conclude that mean arsenic concentration in the drinking water in rural Arizona is different from the mean arsenic concentration in metropolitan Phoenix drinking water. Furthermore, the mean arsenic concentration is higher in rural Arizona communities. The P-value for this test is approximately P 0.016.
CHAPTER 10 STATISTICAL INFERENCE FOR TWO SAMPLES
The Minitab output for this example follows:
Two-Sample T-Test and CI: PHX, RuralAZ Two-sample T for PHX vs RuralAZ N Mean StDev SE Mean PHX 10 12.50 7.63 2.4 RuralAZ 10 27.5 15.3 4.9 Difference mu PHX mu RuralAZ Estimate for difference: 15.00 95% CI for difference: ( 26.71, 3.29) T-Test of difference 0 (vs not ): T-Value 2.77 P-Value
0.016 DF
The numerical results from Minitab exactly match the calculations from Example 10-6. Note that a two-sided 95% CI on 1 2 is also reported. We will discuss its computation in Section 10-3.4; however, note that the interval does not include zero. Indeed, the upper 95% of con dence limit is 3.29 ppb, well below zero, and the mean observed difference is x1 x2 12 5 17.5 15 ppb.
10-3.2 10-3.3
More about the Equal Variance Assumption (CD Only) Choice of Sample Size
The operating characteristic curves in Appendix Charts VIe, VIf, VIg, and VIh are used to 2 2 2 evaluate the type II error for the case where 2 . Unfortunately, when 2 1 2 1 2, the * distribution of T 0 is unknown if the null hypothesis is false, and no operating characteristic curves are available for this case. 2 2 2 For the two-sided alternative H1: 1 and n1 n2 2 0, when 1 2 n, Charts VIe and VIf are used with 0 (10-17) d 2 where is the true difference in means that is of interest. To use these curves, they must be entered with the sample size n* 2n 1. For the one-sided alternative hypothesis, we use Charts VIg and VIh and de ne d and as in Equation 10-17. It is noted that the parameter d is a function of , which is unknown. As in the single-sample t-test, we may have to rely on a prior estimate of or use a subjective estimate. Alternatively, we could de ne the differences in the mean that we wish to detect relative to .
EXAMPLE 10-7
Consider the catalyst experiment in Example 10-5. Suppose that, if catalyst 2 produces a mean yield that differs from the mean yield of catalyst 1 by 4.0%, we would like to reject the null hypothesis with probability at least 0.85. What sample size is required Using sp 2.70 as a rough estimate of the common standard deviation , we have d 2 4.0 3 122 12.702 4 0.74. From Appendix Chart VIe with d 0.74 and 0.15, we nd n* 20, approximately. Therefore, since n* 2n 1, n n* 2 n2 1 20 2 n 1 10.5 11. 111say2